Question

In the following exercises, expand each binomial using Pascal's Triangle.

$(y+1{)}^7$

Short answer

Expansion is$y^7+7y^6+21y^5+35y^4+35y^3+21y^2+7y+1$

Step-by-step solution

Given Information 

Expand binomial using Pascal's Triangle.

$(y+1{)}^7$

Solution

We have

Here the exponent is 7 hence we need to consider eighth row

The expansion is

$$\begin{gathered} (y+1{)}^7=1y^7+7y^6·1+21y^5·1^2+35y^4·1^3+35y^3·1^4+21y^2·1^5+7y·1^6+1·1^7 \\ =y^7+7y^6+21y^5+35y^4+35y^3+21y^2+7y+1 \end{gathered}$$